In mathematics a field of sets is a pair \langle X, \mathcalF \rangle where X is a set and \mathcalF is an algebra over X i.e., a non-empty subset of the power set of X closed under the intersection and union of pairs of sets and under complements of

In other words \mathcalF forms a subalgebra of the power setBoolean algebra of X . (Many authors refer to \mathcalF itself as a field of sets.) Elements of X are called points and those of \mathcalF are called complexes